We consider random Dirac operators on a strip of width 2L of the form $J\partial+V$ where J is the $2L \times 2L $ symplectic form and V a hermitian matrix-valued random potential satisfying a time reversal symmetry property.
The operator can be analyzed using transfer matrices. The time reversal symmetry forces the transfer matrices to be in the group $SO^*(2L)$. This leads to symmetry and Kramer's degeneracy for the Lyapunov spectrum which forces two Lyapunov exponents to be zero if L is odd. Adopting a criterion
by Goldsheid and Margulis one proves that these are the only vanishing Lyapunov exponents under sufficient randomness. Adopting Kotani theory one obtains a.c. spectrum of multiplicity two on the whole real line. If moreover the random potential includes i.i.d., a.c. distributed matrix Diracpeaks on a lattice in $\RR$, we can adopt the work of Jaksic and Last to prove that the a.c. spectrum is pure. This is a big contrast to the case where L is even and no Lyapunov exponent vanishes for sufficient randomness. There one expects to get pure
point spectrum using similar techniques as in the one dimensional Anderson model. (joint work with H. Schulz-Baldes)